The present invention comprises a new and distinct variety of Illicium, hereinafter referred to by the cultivar name ‘NCIH1’. ‘NCIH1’ was selected from a population of seedlings grown from an open-pollinated, F1 hybrid of Illicium mexicanum x Illicium floridanum (2004-318, unpatented). The first asexual propagation of ‘NCIH1’ was carried out in July 2007 by rooting stem cuttings in Mills River, N.C. and has been asexually reproduced repeatedly by vegetative cuttings over a 9-year period. ‘NCIH1’ roots readily from softwood and semi-hardwood cuttings treated with a basal dip of 5,000-10,000 ppm indole butyric acid (potassium salt) in water. Time to rooting for semi-hardwood cuttings is approximately 6 weeks at 30° C. ‘NCIH1’ has been found to retain its distinctive characteristics through successive asexual propagations.